
List of Figures
2.1 Splitting data to be used in the training phase. Image source: [Chollet, 2017] 7
2.2 A Deep Neural Network with N hidden layers . . . . . . . . . . . . . . . . 8
2.3 Basic structure of a neural network . . . . . . . . . . . . . . . . . . . . . . 10
2.4 The red arrows show the change in the value of weight after one step of
mini-batch gradient descent with use of momentum. The blue points show
about the direction of the gradient with respect to the mini-batch at each
step. The Momentum smooths the path taken towards the local minimum
and further leads to faster convergence.[21],[25] . . . . . . . . . . . . . . . 28
2.5 ROC curves depending on the effectiveness of the model . . . . . . . . . . 32
3.1 Feynman diagrams depicting t
¯
tH production modes . . . . . . . . . . . . . 34
3.2 Leading-order Feynman diagram for single T’ production . . . . . . . . . . 35
3.3 ttgg Feynman diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.4 Feynman diagram for ttgg . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5 Feynman diagram of thq . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.6 Simulated sample plot for different variables, for each figure plotted above
the signal is Tprime and the background is tth, thq, and ttgg. From top to
bottom, plots for different variable are as, (a) Plot for Dipho_P
T
, (b) Plot
for Dipho_leadEt, (c)Plot for jet1_e, (d) Plot for b jet1_P
T
, (e) Plot for
jet2_e, (f) Plot for jet3_e, and (g) Plot for jet1_P
T
. . . . . . . . . . . . . 37
4.1 Neural network scheme. Image source: [Chollet, 2017] . . . . . . . . . . . 40
4.2 Basic architecture of our DNN Model . . . . . . . . . . . . . . . . . . . . 42
4.3 Correlation plot of two different datasets for different variables. Above, (a)
Correlation plot for background(ttgg) and below, (b) Correlation plot for
signal(Tprime) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4 Training and testing loss when Tprime is used as signal and ttgg as the
background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.5 Training and testing model accuracy when Tprime is used as signal and
ttgg as the background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.6 Output of training using the DNN(Deep Neural Network). Here signal(Tprime)
and background(ttgg) are clearly separated with background as 0 and signal
corresponds to 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.7 ROC curve for the training out of Tprime as signal and ttgg as the background 48
4.8 Boosted Decision Tree(BDT), ROC curve . . . . . . . . . . . . . . . . . . 49
4.9 Output of training from the DNN(Deep Neural Network). Here signal(Tprime)
and background(ttgg &
¯
tth ) are clearly separated with background as 0 and
signal corresponds to 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.10 ROC curve for the training output of Tprime as signal and ttgg, tth, and thq
as the background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.11 Training and testing model accuracy when Tprime is used as signal and
ttgg, tth, and thq were used as the background. To train different dataset
over a single dataset are known as multi-class classification. . . . . . . . . 51
4.12 Training and testing loss when Tprime is used as signal and ttgg, tth, and
thq were used as the background. To train different dataset over a single
dataset are known as multi-class classification. . . . . . . . . . . . . . . . 52
iv